1. Field of the Invention
This invention relates to finite impulse response (FIR) filters, and more particularly to FIR filters with quantized filter coefficients.
2. Description of the Related Art
FIR filters have come into use as digital filters whose performance typically equals or exceeds that available with passive RLC filters. They can be used in numerous digital environments, such as for removing images of the input signal to a digital-to-analog converter (DAC) that results from increasing the input sampling rate. Such filters are described in general in Fink et al., Ed., Electronics Engineers' Handbook, 3rd Ed. McGraw-Hill Book Co., 1989, pages 8.78-8.80.
A block diagram of a typical FIR filter is given in FIG. 1. A digital input data signal Din, representing an analog signal sampled at a sample rate f.sub.s =1/T, is applied to an input terminal 2. The filter includes M delay stages 4-1, 4-2, 4-3 . . . 4-M, each of which delays the associated sample by the period T. At the initial data node D1 and at the data nodes D2, D3 . . . Dm following each delay stage, the input signal is multiplied by a respective weighting coefficient C(k) in respective multipliers 8-1, 8-2, 8-3 . . . 8-M. The products are summed together in a summer 10 to provide the filter output in discrete time at an output terminal 12. The output Do(nT) at a time nT is given by the expression ##EQU1## this represents the linear convolution of the coefficients C(k) with the input signal. Where c(k) is the sequence of coefficients which defines the filter's impulse response, which is determined as the inverse Fourier transform of the desired filter response in the frequency domain, Do(nT) is the desired filter output in discrete time.
One significant drawback of the FIR filter described above is that, when the input data and filter coefficients have high resolutions with significant numbers of bits, a large amount of hardware circuitry is required to perform the D.times.C convolution. A synchronous filter could be substituted for the FIR filter to reduce the hardware requirements, since synchronous filters use fewer coefficients. However, the attenuation characteristics of a synchronous filter are not as good as those of a FIR filter, and residual portions of the signal at undesired frequencies may propagate through the filter.